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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Isochronous and period-doubling diagrams for symplectic maps of the plane

Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the interpretation of how systems evolve under varying conditions. While the area-preserving quadratic Hénon map has received significant theoretical attention, a comprehensive description of its mixed parameter-space dynamics remain lacking. This limitation arises from early attempts to reduce the full two-dimensional phase space to a one-dimensional projection, a simplification that resulted in the loss of important dynamical features. Consequently, there is a clear need for a more thorough understanding of the underlying qualitative aspects. This paper aims to address this gap by revisiting the foundational concepts of reversibility and associated symmetries, first explored in the early works of G.D. Birkhoff. We extend the original framework proposed by Hénon by adding a period-doubling diagram to his isochronous diagram, which allows to represents the system’s bifurcations and the groups of symmetric periodic orbits that emerge in typical bifurcations of the fixed point. A qualitative and quantitative explanation of the main features of the region of parameters with bounded motion is provided, along with the application of this technique to other symplectic mappings, including cases of multiple reversibility. Modern chaos indicators, such as the Reversibility Error Method (REM) and the Generalized Alignment Index (GALI), are employed to distinguish between various dynamical regimes in the mixed space of variables and parameters. These tools prove effective in differentiating regular and chaotic dynamics, as well as in identifying twistless orbits and their associated bifurcations. Additionally, we discuss the application of these methods to real-world problems, such as visualizing dynamic aperture in accelerator physics, where our findings have direct relevance.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Generalising G 2 geometry: involutivity, moment maps and moduli

We analyse the geometry of generic Minkowski N = 1, D = 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds. In type II theories, they extend the notion of Calabi-Yau geometry and include the class of flux backgrounds based on generalised complex structures first considered by Graña et al. (GMPT). Using E 7(7) × $\mathbb{R}$ + generalised geometry we show that these compactifications are characterised by an SU(7) ⊂ E 7(7) structure defining an involutive subbundle of the generalised tangent space, and with a vanishing moment map, corresponding to the action of the diffeomorphism and gauge symmetries of the theory. The Kähler potential on the space of structures defines a natural extension of Hitchin’s G 2 functional. Using this framework we are able to count, for the first time, the massless scalar moduli of GMPT solutions in terms of generalised geometry cohomology groups. It also provides an intriguing new perspective on the existence of G 2 manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Magnetic-Confinement Fusion—Plasma Theory: Tokamak Magnetohydrodynamic Equilibrium and Stability

Magnetohydrodynamics (MHD) provides a useful model to describe the crucial plasma macroscopic equilibrium and stability behaviors in toroidal tokamak devices by considering the plasma as a conducting fluid interacting with a surrounding confining electromagnetic field. MHD is the most basic plasma model, incorporating most large-scale phenomena, including plasma equilibrium and all major instabilities. MHD equations are obtained by taking moments of the Boltzmann equations for different plasma species. They provide a set of comprehensive physics constrains to compute and optimize the equilibrium plasma shape and pressure and current profiles that are critical to its stability and performance. In the ideal case, the equations have special properties that lead to efficient numerical calculation schemes, the most important of which is the ideal MHD energy principle for linear stability against small departures from equilibrium. In a tokamak plasma, equilibrium pressure is mostly destabilizing for MHD modes, whereas equilibrium current is also often a major driving force. Plasma resistivity creates new freedom for a MHD instability to grow, but there are also cases where the plasma resistivity plays a stabilizing role. Equilibrium toroidal flow and/or flow shear can affect MHD instabilities. Principal MHD instabilities include the internal kink mode, sawtooth, fishbone, external kink, resistive wall mode, resistive interchange, tearing and neoclassical tearing modes (NTMs), locked modes, toroidal Alfven eigenmodes (TAEs), and edge localized modes (ELMs). Fast-growing MHD instabilities can lead to an abrupt plasma disruption and termination that can potentially damage the device plasma facing components (PFCs) and in-vessel structures. Furthermore, an important MHD application is to develop robust techniques to mitigate and control MHD instabilities.

Dispersive pellet injection↗
DOE OSTI2023

Machine learning-assisted crystal engineering of a zeolite

Abstract It is shown that Machine Learning (ML) algorithms can usefully capture the effect of crystallization composition and conditions (inputs) on key microstructural characteristics (outputs) of faujasite type zeolites (structure types FAU, EMT, and their intergrowths), which are widely used zeolite catalysts and adsorbents. The utility of ML (in particular, Geometric Harmonics) toward learning input-output relationships of interest is demonstrated, and a comparison with Neural Networks and Gaussian Process Regression, as alternative approaches, is provided. Through ML, synthesis conditions were identified to enhance the Si/Al ratio of high purity FAU zeolite to the hitherto highest level (i.e., Si/Al = 3.5) achieved via direct (not seeded), and organic structure-directing-agent-free synthesis from sodium aluminosilicate sols. The analysis of the ML algorithms’ results offers the insight that reduced Na 2 O content is key to formulating FAU materials with high Si/Al ratio. An acid catalyst prepared by partial ion exchange of the high-Si/Al-ratio FAU (Si/Al = 3.5) exhibits improved proton reactivity (as well as specific activity, per unit mass of catalyst) in propane cracking and dehydrogenation compared to the catalyst prepared from the previously reported highest Si/Al ratio (Si/Al = 2.8).

36 MATERIALS SCIENCE↗
DOE OSTI2020

Determination of a macro- to micro-scale progression leading to a magnetized plasma disruption

We report here the observations of a plasma jet evolving through a macro- to micro-scale progression sequence. This leads to a fast magnetic reconnection that results in the jet breaking off from its originating electrode and forming a force-free state. A sausage-like pinching occurs first and squeezes an initially fat, short magnetized jet so that it becomes thin. The thin jet then becomes kink unstable. The lengthening of the jet by the kinking thins the jet even more since the kink is an incompressible instability. When the jet radius becomes comparable to the ion-skin depth, Hall and electron inertial physics become important and establish the environment for a fast magnetic reconnection. This fast reconnection occurs, disrupting the jet and establishing a force-free state. X-ray bursts and whistler waves, evidence of a magnetic reconnection, are observed when the plasma jet breaks off from the electrode. This experimentally confirmed sequence of successive thinning from pinching followed by kinking is reproduced in a three-dimensional ideal Magnetohydrodynamic (MHD) numerical simulation. The results of the experiment and the numerical simulation, together demonstrate a viable path from macro-scale MHD physics to micro-scale non-MHD physics where fast reconnection occurs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Chaos as the cause of randomness in tearing mode onset times in DIII-D ITER baseline scenario plasmas

The first evidence of widespread chaotic plasma dynamics relevant to the onset of disruptive tearing modes is found in DIII-D tokamak discharges. This evidence is obtained by calculating positive maximal Lyapunov exponents from Mirnov signals using the Rosenstein algorithm, implying the chaotic growth and/or rotation of magnetohydrodynamic modes in DIII-D [Luxon, Nucl. Fusion 42, 614 (2002)] plasmas. Such chaotic dynamics offer an explanation for the random tearing mode onset times previously observed in ITER baseline scenario discharges. Further, the Lyapunov timescales associated with this chaos could inhibit reliable prediction of tearing mode onset beyond the angular momentum confinement timescale; this constraint should inform the design of plasma control systems on ITER.

Chaotic dynamics↗
DOE OSTI2020

Benchmarking and Improving Microbial-explicit Soil Biogeochemistry Models

Soils represent the largest terrestrial carbon pool on Earth. Yet emerging theories regarding stabilization of soil organic matter remain poorly represented in global-scale models; thus, underestimating the true uncertainty associated with potential terrestrial carbon cycle – climate feedbacks. With this project we created a testbed to compare and evaluate soil biogeochemical models (W. Wieder at the Univ. of CO, Boulder), data synthesis (R. Phillips, Indiana Univ.) and parameter estimation (S Allison, Univ. CA Irvine) to quantify uncertainty associated with potential soil C changes. This project resulted in 14 Presentations, 14 Publications and helped support the training of three graduate students. A significant accomplishment with this work was the creation of a soil biogeochemical testbed, which forces three soil carbon models (CASA, MIMICS, and CORPSE) with common environmental drivers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Machine learned synthesizability predictions aided by density functional theory

Abstract A grand challenge of materials science is predicting synthesis pathways for novel compounds. Data-driven approaches have made significant progress in predicting a compound’s synthesizability; however, some recent attempts ignore phase stability information. Here, we combine thermodynamic stability calculated using density functional theory with composition-based features to train a machine learning model that predicts a material’s synthesizability. Our model predicts the synthesizability of ternary 1:1:1 compositions in the half-Heusler structure, achieving a cross-validated precision of 0.82 and recall of 0.82. Our model shows improvement in predicting non-half-Heuslers compared to a previous study’s model, and identifies 121 synthesizable candidates out of 4141 unreported ternary compositions. More notably, 39 stable compositions are predicted unsynthesizable while 62 unstable compositions are predicted synthesizable; these findings otherwise cannot be made using density functional theory stability alone. This study presents a new approach for accurately predicting synthesizability, and identifies new half-Heuslers for experimental synthesis.

Lee, Andrew (ORCID:0000000153014295)↗
DOE OSTI2021

Surfactants and cloud droplet activation: A systematic extension of Köhler theory based on analysis of droplet stability

The activation of aerosol particles to form cloud droplets, a necessary first step in cloud formation, controls much of the impact that aerosols have on clouds and climate. Recently, there has been a surge of interest in extending the Köhler theory of cloud droplet activation to include surface active (typically organic) as well as water-soluble (typically inorganic) aerosol components, but a systematic framework for doing this has yet to be developed. Here, we apply a droplet stability analysis to this end. Ideal and Szyszkowski–Langmuir surfactant models are analyzed to demonstrate the new approach, but the underlying theoretical framework is fundamental and model free. A key finding is that superficial densities at the cloud activation threshold (Köhler maximum) are significantly sub-monolayer, with fractional coverage ranging from 69% to 85% for the organic compounds and mixtures studied. The result, significant for model inventories of cloud condensation nuclei, is a weakening of the surfactant effect relative to expectations based on bulk sample measurements. Analytical results are obtained for the loci of Köhler maxima and applied to aerosol mixtures containing an arbitrary number of water-soluble and surfactant components.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Design of super-strong and thermally stable nanotwinned Al alloys via solute synergy

Al alloys have widespread industrial applications. However, their mechanical strength is often much lower than steels. Here, we investigate the influence of solutes on achieving ultrahigh strength and thermal stability of nanotwinned Al alloys. In situ micropillar compression tests show the addition of a small amount of Ti can significantly increase the mechanical strength of Al–Ni alloys to 2 GPa. Deformation induced detwinning, Ni segregation and grain coarsening as discovered in binary Al–Ni alloys are mostly absent in the ternary Al–Ni–Ti alloys. Moreover, the ternary Al–Ni–Ti alloys have outstanding thermal stability. Density function theory calculations reveal the synergetic pinning effect of Ni–Ti solute pairs on incoherent twin boundaries. This study demonstrates that the proper selection of synergistic solute pairs is critical to improve the thermal stability and mechanical properties of nanotwinned Al alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Diffusion energy barrier of Au on Bi 2 Se 3 : theory and experiment

The stability and diffusion of ultra-thin thermally deposited Au films on Bi 2 Se 3 was studied using scanning tunneling microscopy and density functional theory calculations. The Au/Bi 2 Se 3 interface is of interest as gold is predicted to provide excellent electrical contact while maintaining the spin-polarized characteristics of the electronic states in Bi 2 Se 3 that make the material attractive for spintronic applications. When deposited at room temperature, Au 10 covers the surface with tightly packed islands of nanometer scale dimension. The surface morphology is stable up to 400K. At this annealing temperature, Au atoms have sufficient energy to diffuse across the surface and aggregate into larger nanostructures. At 550K, the Bi 2 Se 3 surface is only sparsely covered, and the Au has formed clusters with length scales 5-10 times larger than the original islands formed at room temperature. Comparison of the experiment and first principle calculation lead to the conclusion that the diffusion energy barrier for Au on Bi 2 Se 3 is as high as 0.47 eV, 15 which is much larger than diffusion barriers on other van der Waals materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Hofmann Stability Charts Revisited for PIP-II: From Classical Theory to Assumption-Free and ML-Driven Maps

The Hofmann stability chart remains a standard for visualizing parametric resonances in space-charge–dominated linacs, but its use typically relies on non-oscillatory Vlasov dispersion relations with simplifying assumptions (continuous focusing, KV phase space, linear optics, limited transverse–longitudinal coupling). We revisit the chart for the PIP-II linac along three tracks. (1) We reproduce the conventional maps in the (νz/νx, νx/ν0x) plane for relevant εz/εx, providing a validated reference. (2) We remove key assumptions by deriving stability surfaces directly from multi-particle tracking with realistic lattice discreteness, RF defocusing, solenoid/quad optics, and bunched-beam dynamics; local tunes and early-time growth rates are estimated from envelope oscillations and projected to the same coordinates. These assumption-reduced maps recover the canonical stopbands while revealing shifts and broadenings driven by tune modulation, non-KV distributions, and transverse–longitudinal coupling at PIP-II intensities. (3) We train a compact machine-learning surrogate that emulates the growth surface from zero-current optics, tune depression, emittance ratio, bunching factor, and selected lattice descriptors, enabling rapid scans and online working-point selection. We compare the three representations on representative PIP-II sections and discuss implications for commissioning guard bands, resonance avoidance, and routine operations.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗
DOE OSTI2023

Structural Stability of Graphene-Supported Pt Layers: Diffusion Monte Carlo and Density Functional Theory Calculations

In this study, we used a combination of diffusion Monte Carlo and density functional theory calculations to investigate the stability and interlayer binding of various layered structures of Pt atoms adsorbed on graphene. Our findings show that vertically buckled Pt monolayer and bilayer with (111)-packing order are more energetically favorable than the corresponding buckled (100) or flat (100)-packing structures. This can be attributed to the significant lattice mismatch (>10%) between pristine graphene and a free-standing (100)-packing Pt layer. Additionally, our calculations reveal that among the (100)-packing Pt layers, an incommensurate structure with a Pt/C atomic ratio less than 1/2 may be more stable than the commensurate structures registered at the bridge sites, which aligns with recent experimental findings of incommensurate (100)-packing Pt layers on graphene. The interlayer binding between the Pt layer and graphene is found to be primarily driven by van der Waals interaction, except for the AA-stacked buckled-(100) Pt bilayer where the bottom Pt atoms show chemisorption to the graphene surface. In conclusion, this research offers a comprehensive examination of the stability and interlayer binding of metallic Pt layers, providing valuable insights for potential applications as a next-generation catalyst.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Enhanced Synchronization Stability of Grid-Forming Inverters With Passivity-Based Virtual Oscillator Control

In this article, a passivity-based virtual oscillator control strategy with enhanced synchronization stability for grid-forming inverters (GFMs) is proposed. By adopting the port-controlled Hamiltonian system theory for orbital stabilization problems, an energy pumping-and-damping block is proposed to render GFMs globally asymptotically stable with respect to the prespecified solutions of the power-flow equations from any initial condition. This allows for stable integrations of GFMs to any other globally asymptotically stable systems without their explicit knowledge, e.g., helping maintain synchronism with the bulk power system in a wide range of short-circuit-ratio conditions or under large disturbances and keeping synchronism among multiple GFMs in power systems. Herein, both simulations and experiments are presented to demonstrate the proposed control approach.

42 ENGINEERING↗
DOE OSTI2021

Microstructure-dependent rate theory model of defect segregation and phase stability in irradiated polycrystalline LiAlO 2

We report gamma lithium aluminate (LiAlO 2 ) is a breeder material for tritium and is one of key components in a tritium-producing burnable absorber rod (TPBAR). Dissolution and precipitation of second phases such as LiAl 5 O 8 and voids are observed in irradiated LiAlO 2 . Such microstructure changes cause the degradation of thermomechanical properties of LiAlO 2 and affect tritium retention and release kinetics, and hence, the TPBAR performance. In this work, a microstructure-dependent model of radiation-induced segregation (RIS) has been developed for investigating the accumulation of species and phase stability in polycrystalline LiAlO 2 structures under irradiation. Three sublattices (i.e. [Li, Al, V] I [O, V o ] II [Li i , Al i , O i , V i ] III ), and concentrations of six diffusive species (i.e. Li; vacancy of Li or Al at [Li, Al, V] I sublattice, O vacancy at [O, V o ] II sublattice, and Li, Al and O interstitials at [Li i , Al i , O i , V i ] III interstitial sublattices; are used to describe spatial and temporal distributions of defects and chemistry. Microstructure-dependent thermodynamic and kinetic properties including the generation, reaction, and chemical potentials of defects and defect mobility are taken into account in the model. The parametric studies demonstrated the capability of the developed RIS model to assess the effect of thermodynamic and kinetic properties of defects on the segregation and depletion of species in polycrystalline structures and to explain the phase stability observed in irradiated LiAlO 2 samples. The developed RIS model will be extended to study the precipitation of LiAl 5 O 8 and voids and tritium retention by integrating the phase-field method.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Kinklike structures in an arcsin real scalar dynamics

Highlights: • Kinklike analyses in a real scalar theory with an arcsin dynamic. • First-order formalism implementation and deformation procedure in an arcsin scalar dynamics. In this paper, we analyze kink-like analytical solutions in a real scalar theory with an arcsin dynamics inspired by the arcsin electrodynamics presented in Kruglov (2015). This analysis is done by means of the first-order formalism. This formalism provides a framework where the equations of motion can be simplified by preserving the linear stability of the theory. In this work, the deformation procedure is implemented with the aim of finding exact solutions in systems with generalized dynamics. Along the paper, we explore how the first-order formalism is implemented in the arcsin kinetics and how such a term influences the kink-like solutions. As a part of the result of our paper, we show that the kink-like solutions are similar to the ones obtained in the standard scalar kinetic theory. We also show that the extra parameter, that controls the non-linearities of the model, plays an essential role in the energy densities and stability potentials. These quantities vary according to this parameter. The goals here are to show how the first-order framework is implemented in this arcsin scenario and to present the analytical kink-like solutions that can be found by means of the first-order framework and deformation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Perfect spinfluid: A divergence-type approach

We present a new formulation of nondissipative relativistic spin hydrodynamics that incorporates spin degrees of freedom into the divergence-type theory framework. Due to the divergence-type structure, it is straightforward to enforce nonlinear causality and symmetric hyperbolicity of the equations of motion, ensuring local well-posedness of the initial-value problem and stability of the theory. Furthermore, in a specific realization based on spin kinetic theory, we prove that the equations of motion remain nonlinearly causal and symmetric-hyperbolic to all orders in the spin potential, provided a specific thermodynamic constraint is satisfied. Here, this framework can be applied for numerical simulations to study the dynamics of spin-polarized fluids, such as the quark-gluon plasma in heavy-ion collisions.

Chirality↗